{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make toy data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Type 1. Independent Gaussian\n",
    "\n",
    "$$\n",
    "(x_1, x_2) \\sim \\mathcal{N}(0,I)\n",
    "$$\n",
    "\n",
    "## Type 2. Correlated Gaussian\n",
    "\n",
    "$$\n",
    "(y_1, y_2) \\sim \\mathcal{N}(0,\\begin{bmatrix}1&\\rho\\\\ \\rho&1\\end{bmatrix})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.multivariate_normal( mean=[0,0],\n",
    "                                  cov=[[1,0],[0,1]],\n",
    "                                 size = 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.random.multivariate_normal( mean=[0,0],\n",
    "                                  cov=[[1,0.8],[0.8,1]],\n",
    "                                 size = 300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9bee40e898>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt indep Gaussian\n",
    "sns.scatterplot(x=x[:,0],y=x[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9bee34f828>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt cor Gaussian\n",
    "sns.scatterplot(x=y[:,0],y=y[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define MINE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "import torch.autograd as autograd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Mine(nn.Module):\n",
    "    def __init__(self, input_size=2, hidden_size=100):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(input_size, hidden_size)\n",
    "        self.fc2 = nn.Linear(hidden_size, hidden_size)\n",
    "        self.fc3 = nn.Linear(hidden_size, 1)\n",
    "        nn.init.normal_(self.fc1.weight,std=0.02)\n",
    "        nn.init.constant_(self.fc1.bias, 0)\n",
    "        nn.init.normal_(self.fc2.weight,std=0.02)\n",
    "        nn.init.constant_(self.fc2.bias, 0)\n",
    "        nn.init.normal_(self.fc3.weight,std=0.02)\n",
    "        nn.init.constant_(self.fc3.bias, 0)\n",
    "        \n",
    "    def forward(self, input):\n",
    "        output = F.elu(self.fc1(input))\n",
    "        output = F.elu(self.fc2(output))\n",
    "        output = self.fc3(output)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mutual_information(joint, marginal, mine_net):\n",
    "    t = mine_net(joint)\n",
    "    et = torch.exp(mine_net(marginal))\n",
    "    mi_lb = torch.mean(t) - torch.log(torch.mean(et))\n",
    "    return mi_lb, t, et\n",
    "\n",
    "def learn_mine(batch, mine_net, mine_net_optim,  ma_et, ma_rate=0.01):\n",
    "    # batch is a tuple of (joint, marginal)\n",
    "    joint , marginal = batch\n",
    "    joint = torch.autograd.Variable(torch.FloatTensor(joint)).cuda()\n",
    "    marginal = torch.autograd.Variable(torch.FloatTensor(marginal)).cuda()\n",
    "    mi_lb , t, et = mutual_information(joint, marginal, mine_net)\n",
    "    ma_et = (1-ma_rate)*ma_et + ma_rate*torch.mean(et)\n",
    "    \n",
    "    # unbiasing use moving average\n",
    "    loss = -(torch.mean(t) - (1/ma_et.mean()).detach()*torch.mean(et))\n",
    "    # use biased estimator\n",
    "#     loss = - mi_lb\n",
    "    \n",
    "    mine_net_optim.zero_grad()\n",
    "    autograd.backward(loss)\n",
    "    mine_net_optim.step()\n",
    "    return mi_lb, ma_et"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_batch(data, batch_size=100, sample_mode='joint'):\n",
    "    if sample_mode == 'joint':\n",
    "        index = np.random.choice(range(data.shape[0]), size=batch_size, replace=False)\n",
    "        batch = data[index]\n",
    "    else:\n",
    "        joint_index = np.random.choice(range(data.shape[0]), size=batch_size, replace=False)\n",
    "        marginal_index = np.random.choice(range(data.shape[0]), size=batch_size, replace=False)\n",
    "        batch = np.concatenate([data[joint_index][:,0].reshape(-1,1),\n",
    "                                         data[marginal_index][:,1].reshape(-1,1)],\n",
    "                                       axis=1)\n",
    "    return batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9bb5a4b940>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "joint_data = sample_batch(y,batch_size=100,sample_mode='joint')\n",
    "sns.scatterplot(x=joint_data[:,0],y=joint_data[:,1],color='red')\n",
    "marginal_data = sample_batch(y,batch_size=100,sample_mode='marginal')\n",
    "sns.scatterplot(x=marginal_data[:,0],y=marginal_data[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(data, mine_net,mine_net_optim, batch_size=100, iter_num=int(5e+3), log_freq=int(1e+3)):\n",
    "    # data is x or y\n",
    "    result = list()\n",
    "    ma_et = 1.\n",
    "    for i in range(iter_num):\n",
    "        batch = sample_batch(data,batch_size=batch_size)\\\n",
    "        , sample_batch(data,batch_size=batch_size,sample_mode='marginal')\n",
    "        mi_lb, ma_et = learn_mine(batch, mine_net, mine_net_optim, ma_et)\n",
    "        result.append(mi_lb.detach().cpu().numpy())\n",
    "        if (i+1)%(log_freq)==0:\n",
    "            print(result[-1])\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ma(a, window_size=100):\n",
    "    return [np.mean(a[i:i+window_size]) for i in range(0,len(a)-window_size)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.00020082519\n",
      "2.719705e-05\n",
      "-2.857225e-06\n",
      "-7.3535484e-06\n",
      "4.3286927e-06\n"
     ]
    }
   ],
   "source": [
    "mine_net_indep = Mine().cuda()\n",
    "mine_net_optim_indep = optim.Adam(mine_net_indep.parameters(), lr=1e-3)\n",
    "result_indep = train(x,mine_net_indep,mine_net_optim_indep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.572848e-06\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9b9e98e940>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_indep_ma = ma(result_indep)\n",
    "print(result_indep_ma[-1])\n",
    "plt.plot(range(len(result_indep_ma)),result_indep_ma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6552668\n",
      "0.4192042\n",
      "0.5817597\n",
      "0.52291673\n",
      "0.75059044\n"
     ]
    }
   ],
   "source": [
    "mine_net_cor = Mine().cuda()\n",
    "mine_net_optim_cor = optim.Adam(mine_net_cor.parameters(), lr=1e-3)\n",
    "result_cor = train(y,mine_net_cor,mine_net_optim_cor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.52786046\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9b9b28cf28>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jp+3RtMeGqsZnYz2dFMh+Q3vTo7ThM3nk+c/jOmnd6uqDfL1lF+FwOC51MnbfvrHb0XTCHr1K4p77z7cb/yZ6lxVhBvdknOv5UaOdvP/VzhmDvy7I02+u4J6nFvHYi5Eyulu40d9VMsFQmHm2kmBCR0905NCkMZEOzwefWxKXIluxbht3//0Tnnoj8tne7swMnuhKPbZW4tnJbU10/jYn2omcbMCD+++hLULhMG98vC5uRNjuosCfIc+/twq7emvSVfkuv/utlKkM9/T3q+9/l0ef/yzutBVgyw5/0lmE3bp24dcXHxo7LU22Xnp0nZWoX/xoLMWFyVfjzs+Lb3G94gz1XL6uoU5dkoxL7p5ibRWIdLZdfPsbcSmEVU6dJ47qF9fRZlvYigJiSxHs7bT23BON0p12f/ffP+H3z37KLx79gH++9SV/eW0ZO2vrWOTMurzzJ4c3ynMn0zPhABhtfQPcl+LiHj+9523+38Nz+d3fFsb26VVWxHBX69X9GZ113D6x28Fg4wPlTn99LMWQaEDCcMwPPvuaVz5sOHOZ9rs5rN0UOVieOnFoo9+hW3QW75KVW5KOfHGPdKlypa/eXLiexUlSgJ9kYIar+2ALpPWdpeI++0hc7iLVaKZkfnnBuNjf1b1PL4rVPRwOs9wVK9JtpGSKAn8G7Kqt45m3vuS2vyzg8VeSjwJ5JMVRPXGSzbufbuQ9J4BHg+w7izbEhj66J9EcYvqmDOKJHr3+WB65/lj26t895T79y+NblAGns7awoOk/oHRys+4hftE/hIF9Imcj+zsjje6YtYDL744fxdLUWUAwFKLKycF3ccp4xfcPjHU+znq96Vx/MBSKG2USbcUH6kOsch1o3WdDAEekCIh79I7//O676qjY6JolK5N3+Ef7X9wH6FsvmcDx45JPZDraGR8O8cMOIdIxv65yJ199nXypgeGDesTd/9NLSxt9vjP+GTn4HLZ/v7RSLy++/xWXJYw8mnhAP/ol/JaaM9ZUtGj/VM6ZNDwjrwNgBkeGxUYbQFHRPol01tzfs18Z5zr9YAu/2Bw7m//1zHnc9pcFsf0W7ealHRT4MyCdiTG1KZZFiHaqugVDYfbq3z1pWsUdXGqcvP8Be/du8r3Hj9wDn89HXjN/yD8/ezQXfXc/HrzmaADe+mQDtYF6nnsnMuMzMXBE5eflxdI9p04cysPXHcN9V8Wvr3LVfQ05/OqaeooK82MHttNcIyNq/MFYMLz5jx9y8W1v8Nw7K5OO+vn3u6sabevbq4Tf/XRi3LZAXbBRuikcDnPLn+Zxy5/iD7wQSZl9nnCm5HaGU94zjxkW23bN2aOTfr6Xn9GQfrjvmcVx4/8T0yRRRYX55Pl83H/VkdyTMGplz37dufuKIygpKoiNf4+KvnaqJQyAlDNjEyWevSS6zhn1smzttkaPHWL6kp+Xx6PXHxu3/4SRe8Tt938/O4LRw/tw3JhBnO06k2mLEw8dwlVnHRS30FtrRdM9qZZYTvdiK4mzd0PhcFzDYt8hPTl0vz0Sn9auFPgzINkwtP/72RGMGtYwYSa6/odbKBxm87Za9tyjjN9eGt9xF00BDekbn6N3B5dBfcti26Z8O9KZ94Njh8dNZ4f0c5I9S4uYeGD/uFPk1+c1zA+45gejUz73d5dP5LEbJnH6kXtTkJ+X9DMJhcI8+vxnvDZvTdxMyn4JLeVtTp559deRkRPPvbMy6aSgfzmBf5+EA5L7M/LXBZn2uzk88vxnce/5+vy1Ta678+LcSKvurGOHNXqsV1kRj90wKTZaBJJ/vxDpAHe78eG5BEMhtu7wx+rn5k63lRR3SZpG69GtkNKSLuyoie94jF4k5aqzDkpVLSYfvw+P3TApdpYFxI3MiipqJk1i9kw9HySamnKfMfQoLYobBnz9uQdTVlLIz84cxXknjmj2/Vpi1LDyJs9s03XpqSMBGOz6G9zuDBVO9X0nk/gdfrJ8c9xZ43WTD26yn6w9KPC30Yr12xpNGrnhvDGUlRRy1VkHccdlh9OtuCBpiz8azL76egd79C6J63SN/hBunnpobFt0unp03P1hBzT8eI4ZPZDHbpjEt8dHHnOHm5suaHnr5yenR0aluDuViwpb9sd5YULn4MfLKpP2Q3QrLmD/vXrHOgSTjXt2nzEA1Lo6zJMFrqhoGmLuZ19z2V1zWLVxOw/8c3GzaaCo74zfs8nHrztnND/7/qi0U24QOZO6Zsa7sTTfoIqG3Hu6K1Fu2lrDh59vikvVvLs48tkmHkiTmeRKGQ3s0437rzqKw/ZPv9WZ5/PF1mqC+HIn+51U9CxmiWvyWGkbJ+3tDsWFBfQqK4obwfOEk8otKUp/zsGBe5cz9aSG4bRzPlnP9p0BepUVMePqo1o9mqktFPjbyD1c8qxjhjHttP0ZMbhhynx5j2J21tbHLiDtttPpJIoGyOLCAm44bwzHjhnI7Zc1jEi4+cJx/PKCcbFTz5MPG8qlp45sstV1648ncPLhQ7n7iiMarbGSjq4J09jd5UnXkQcN4LEbJjFmRCR/m+qyfT6fj2vOHs2RoyIToG77y4KkqR13B/dZN74Qu50s0P3szOSTdD78fBPzbONc+/XnHswtUw/l4pPTG+8etd/Q3rHRMqlM//EEJo0ZGPtMn0joB4qmDAry8xp97s351R8/Yl1lddy4/rKS5oNSset9okNVv3XokCae0diprlFU7g5odwf7lWeO4tSJQ+lSkM9lTmMCoKwdr9ubSe40T119kPnOb+eUJmbsJnPEqP6xg+OiFVVUflPDXv27t/j7zhQF/jZyz+z8zoQ9U+bqkp3WR88UlrkW3xoxuCc/PNHExsoDDNmjjD1dq/91LSpgwsh+jdIIbnv0KuF7R+2d8mpGzTEJ67306dG1Va8DxFY9dLecfn5243REn54N/R3JWv3RpRkSx68nG72RmCKLetnVH1PYJY/vjB/CGUftjRnSi0F9S9sl19q3Vwnnn2hSLjB28D4V/PeUQ/j9NckfTyY6GWnNpuq4NZcK8vPSakG6O4ajLfS+vSLfcbKhoMkkjqK598ojuf2yw+J+lwcN7xMbjlrh6s/q1jU7Aa+lDt0v8lnU+Ov5o+vqX8MHJu/vaop7lNeGql2UZvEz6ByffgcWndkZ/YEk0624gJ219YRC4bg/imjAcp8hdBQF+XncMvVQbnrsw7gcZ2uMH7lH3B/N/0wZGxt+6datuAsF+XnUB0Oxyzpe8f0D466vGgqF465xmqoTr2dp8znTW6YeSt+EsfEF+Xk8dsMkqrbVxh3UM6VXWVGjzsK8PB/DBrQskLgbAm63Xjo+6fZEiQuTQeSM89ZLJ8SNu2/Kwfv04chR/Tl1YuSMpbRrlybX2ynsks9xYwax98DucQ2bjmzcvn358PNNfPDZ18xtYlmUdPh8Pr531N6x9OnWHZlbWqSl0gr8xpgRwEygHKgCplhrlyfsczPwEyC6sPu71trLM1fUjse9NMK00w5Iud+E/fvxn/lreXvReo4e3TC+eVBFN+YtjQyd64gG9S1t1FHcGokt8mRBP2rSmIG8+tGa2AzSvft358ozR/F/Ty8CiLvm6i1TD2VQioNSXp6PK753IBW9uvLUGysajR2fdtr+jYK+W3mS0VaZcOP5h/D4K5ZLTx1JSVFBq/O7yWbUDh/UI+0zs+josLEJrft0+geifD4fF57UstTYeSem7o/piEYNi6Tx3Gfl6Y7mScY9G3zMiKZThO0p3Rb/g8AMa+2TxpjzgYeAZBHhcWvttRkrXQf3+vzI5JdDmhmDHG1dvfXJhrjAv2NXHV2LClJOi88l/XqXsHHLrmZHWyROlulRWsRBw4sYM6KCj5dVxq38mDhuPtHBTt9CNIVU2rVLbCLd7h4+F1Xeo5irf5B61E1L/PbSCeTn+fgvZzmNkU30+SSTiYN6rosOOXa39r97WNMd/k0JuJc2T7Ko3+7SbMQxxvQFxgCznE2zgDHGZGjGRScWXajptIlNtwCiLYSVG7YTCodjnZT/mb+22eUccsVvLhnPjecf0uz46okHJp8clWyRsWSziJOJjh8/94TIWPFMBd5s26N3CX16NrTwd/eQQC8685hhbWqoRSf03XTB2KyM5olKp8U/GFhnrQ0CWGuDxpj1zvbE4RHnGGNOBDYCv7TWvk8LlJe3PpdcUZE859leFq/YHFsKefTI9GY5Ajw/dzXPzlnBcFdevy1l3931bou+fZsf+3zBqQfw+vy1sQlXqer37O2nkJ/mH2BFRRn/Pjgycenko4Zn9Q8uExI/k/uuPZa/vWY5Y9KItD+Tzihbv/WjRg/kLeeKXseOG9Kmcpx2bClHjx1CrzT7UaB96p3Jzt0Hgd9Ya+uMMScAzxlj9rPWpj0XuaqqulWXKauoKKOyMvk09fZyo2v1ys2bm1+i9Tvjh/DSB5GgD/CFs07HYfv3a3XZs1Hv3eEP1x3DRbe9wdGjB8TV7zeXjOfXM+cxfdph5Ofn5WTdm5PsO+9W4GPqd/Zly5aOd6WnTMnmb33siD6xwF+UR0bKUVmZ3no/zdU7L8/XqgZzOoF/DTDQGJPvtPbzgQHO9hhr7UbX7deMMWuAA4D4hTxyTLJhicmkSku8v2Qjl5wyMpNF6vR8Ph8PX3dMo+Gq/cu78cDPj85SqcSrDti7nCvPHMXIob2aXfaks2j2vNBauwlYCEx2Nk0GFlgbPwvGGDPQdXs0MBRI/8KXnYS/Lsjv/hpZXGlI31IO2Cu965hGZ9Qm6qgjerKtID8vZ/7IpPM7aHif2EKAuSDdVM80YKYx5iZgKzAFwBjzInCTtXYecKsx5hAgCASAH7rPAnLF3CUbWeIs4JW4amNT3FP6uxUXcNJhe7Kzpp4TD01v0SwRkUxJK/Bba5cCjWaGWGtPct3+UQbL1WG5L8Bx4UmpL1TRlNOO2Ivj01wlUUQk03J3CEA7ePmD1bz60Rry8yLX+Ux10fFUznGWnm1q4pCISHvTkg0tEF1bZ8gepa2a2Xn82EEMrOjW4ok2IiKZpMDfCis3tG44V57Px/5Dm75oiohIe1OqJ01fuK40tO+QjreomohIutTiT1P0ikwjh/bi52envhKViEhHpxZ/mjZURWZF/uT0AzS+XEQ6NQX+NFTX1PH11hqg8ZWpREQ6GwX+NLz0QSTNc/Lhe3b6Bb5ERNR8bcafX1vGf+ZHrhXb3IW3RUQ6A7X4m7Chamcs6IPSPCKSGxT4m/CN69qoPz51/yyWREQkcxT4E8xdspE3nbW3P18dWTN/yrcM40dm51J9IiKZptwFsHHLLnqVFvHPt7/k1Y8ilxmYeEA/igsjy7BO2F9BX0Ryh6cD/xOvWN5YEGndF+T7qA82XP1r+p8X0KdHMd2KC+KWVBYR6ew8G9FC4XAs6ANxQR8iF0ZfuWE7Bw1L70IrIiKdhWdz/J9/tTXp9uvPPTju/l79m79AuIhIZ+LZwB8dsXPOpOFx282QXpxy+NCGDZqvJSI5xrOBf9vOAABHHjSAy884AIDjDhkEwBlH7c25x0cumqLRPCKSazyZ41+ycgtPv7kCiEzKGjWsD2ccuVcs8AMcP3awLo8oIjnJk4H/hfdXxd3vUpDHKRP3ykpZRER2N0+mepY6E7N+cOzwZvYUEck9nmzxl3cvYsTgnnx7/JBsF0VEZLfzXIu/rj7Ilu1++vYqyXZRRESywnOBf2t1gDBQ3r0420UREckKzwX+HbsiwzjLSrpkuSQiItmRVo7fGDMCmAmUA1XAFGvt8hT7GmAB8IC19tpMFTRTqnfVAVCqwC8iHpVui/9BYIa1dgQwA3go2U7GmHznsWczU7zMq66JBP6yksIsl0REJDuaDfzGmL7AGGCWs2kWMMYYU5Fk9xuA54FlGSthhu1wWvxlXdXiFxFvSifVMxhYZ60NAlhrg8aY9c72yuhOxpiDgG8BxwK/aE1hystLW/M0ACoqytLaL0hkCebBA3vmxIXT0613LvJq3VVvb2mPemdkHL8xpgvwMHChc2Bo1etUVVUTCoWb3zFBRUUZlZU70tp3U9VOSrt2YfPm6ha/T0fTknrnGq/WXfX2lubqnZfna1WDOZ0c/xpgoJO/j+bxBzjbo/oDw4AXjTGrgKuAS4xkMUqeAAAPWklEQVQxD7e4RO2suqaObkrziIiHNdvit9ZuMsYsBCYDTzr/L7DWVrr2WQ30id43xtwMlHbEUT01/npKijw5YVlEBEh/VM804ApjzDLgCuc+xpgXjTFj26tw7aHGH6SrAr+IeFhaEdBauxQYn2T7SSn2v7ltxWo/u/x19O+j5RpExLs8N3NXLX4R8TpPBf5wOMyuWuX4RcTbPBX4A3UhQuGwAr+IeJqnAv8ufz2AUj0i4mkK/CIiHuOpwF/jBP6SYgV+EfEuTwX+XbVq8YuIeCrwx1r8Cvwi4mGeDPxq8YuIl3kq8PvrggAUdcnPcklERLLHk4G/sIunqi0iEsdTEdBfFyQ/z0dBvqeqLSISx1MRMBAIKc0jIp7nqcDvrw9SVKjALyLe5qnAH6gLUqgWv4h4nKcCvz8QpKjAU1UWEWnEU1HQXxekUKkeEfE4TwX+QL06d0VEPBX4/XVBBX4R8TxvBf5AUJO3RMTzPBUFA2rxi4h4K/D7leMXEfFO4A+HwwQCGscvIuKZwF9XHyIMFCnHLyIe55ko2LAyp1r8IuJtaV2RxBgzApgJlANVwBRr7fKEfS4ErgZCQD7wB2vtvZktbusF6kKA1uIXEUm3xf8gMMNaOwKYATyUZJ9/AAdZa0cDhwPXGGNGZaaYbaeLsIiIRDQb+I0xfYExwCxn0yxgjDGmwr2ftXa7tTbs3C0BugBhOggFfhGRiHRSPYOBddbaIIC1NmiMWe9sr3TvaIw5FfgtMAz4f9baxS0pTHl5aUt2j1NRUdbk4xu3+wHoW1Ha7L6dSS7VpaW8WnfV21vao94Zveq4tfZfwL+MMUOAZ40xL1prbbrPr6qqJhRq+UlCRUUZlZU7mtxnk/N4zS5/s/t2FunUO1d5te6qt7c0V++8PF+rGszp5PjXAAONMfkAzv8DnO1JWWtXAx8CJ7e4RO3Er85dEREgjcBvrd0ELAQmO5smAwustYlpnv1ct/sAxwItSvW0p9pAPaDALyKSbqpnGjDTGHMTsBWYAmCMeRG4yVo7D7jUGHMiUAf4gPutta+2Q5lbRcM5RUQi0gr81tqlwPgk209y3b46g+XKOI3qERGJ8MzM3dpAEB9oWWYR8TzPREF/IEhRYT4+ny/bRRERySrPBP7aQD1Fut6uiIh3Ar+/LkhxYUanLYiIdEqeCfy1gSDF6tgVEfFW4FeqR0TEQ4HfHwhSrMAvIuKhwK8LrYuIAB4K/IF6BX4REfBS4K8LafKWiAieCvxBXW9XRASPBP5QOEygPkRhgSeqKyLSJE9Ewrp6rcwpIhLlicAfcFbmVKpHRMQjgT/a4u+iVI+IiDcCvz/W4vdEdUVEmuSJSBi7+laBUj0iIt4I/PXK8YuIRHkj8DstfqV6REQ8E/idFr9SPSIi3gj8/np17oqIRHkiEtZFUz1q8YuIeCPwB+qV4xcRifJEJNTMXRGRBp4I/NEJXJq5KyICBensZIwZAcwEyoEqYIq1dnnCPr8AzgGCQB1wo7X2lcwWt3WiK3Pm+XzZLoqISNal2wR+EJhhrR0BzAAeSrLPh8A4a+0oYCrwN2NM18wUs20CdUG19kVEHM1GQ2NMX2AMMMvZNAsYY4ypcO9nrX3FWrvLubsI8BE5Q8i6yNW3lN8XEYH0Uj2DgXXW2iCAtTZojFnvbK9M8ZwpwApr7dqWFKa8vLQlu8epqChL+ZgvP4+S4oIm9+mscrFO6fJq3VVvb2mPeqeV428JY8zRwK+BE1r63KqqakKhcIvfs6KijMrKHSkf31HtJ9/na3Kfzqi5eucyr9Zd9faW5uqdl+drVYM5ncT3GmCgMSYfwPl/gLM9jjHmMOBJ4HRrrW1xadpJoF7X2xURiWo28FtrNwELgcnOpsnAAmttXJrHGDMO+BtwprX240wXtC0iOX517oqIQPqpnmnATGPMTcBWIjl8jDEvAjdZa+cBDwBdgYeMMdHn/dBauzizRW65QF2Q0q5dsl0MEZEOIa3Ab61dCoxPsv0k1+1xGSxXRvnr1eIXEYnyRDQM1AW1QJuIiMM7gV8tfhERwCuBv14TuEREonI+8AdDIerqQxQr8IuIAB4I/P5AZC3+okIFfhER8ELgd5ZkVuAXEYnI+cBfG6gHUKpHRMSR84FfLX4RkXi5H/gDkcCvFr+ISETOB/7aQLTFn/GFSEVEOqWcD/xK9YiIxMv5wF+rVI+ISJycD/z+gFr8IiJuOR/4a51UT7ECv4gI4IHA7w8Eyc/zUZCf81UVEUlLzkdDfyCo1r6IiEvOB/7aunrl90VEXHI+8PsDQYo0okdEJCbnA39tnVI9IiJuOR/41eIXEYnnicBfrOUaRERicj7w19YF1bkrIuKS84FfqR4RkXi5H/jVuSsiEienA384HFaLX0QkQVq9nsaYEcBMoByoAqZYa5cn7HMicCtwIHCftfbaDJe1xQL1IcJonR4REbd0W/wPAjOstSOAGcBDSfb5ErgYuCNDZWszrcwpItJYs4HfGNMXGAPMcjbNAsYYYyrc+1lrv7DWLgTqM17KVoquzKlUj4hIg3RSPYOBddbaIIC1NmiMWe9sr8xkYcrLS1v93IqKskbbqutCAPTtU5r08VyQq/VKh1frrnp7S3vUu0PNbKqqqiYUCrf4eRUVZVRW7mi0fePXkW3+2kDSxzu7VPX2Aq/WXfX2lubqnZfna1WDOZ0c/xpgoDEmH8D5f4CzvUOrrYtknYq7dKjjm4hIVjUb+K21m4CFwGRn02RggbU2o2me9qDOXRGRxtJtCk8DZhpjbgK2AlMAjDEvAjdZa+cZY44A/gp0B3zGmHOAi6y1r7RDudNSq8AvItJIWoHfWrsUGJ9k+0mu2+8AgzJXtLbzR6+3q1E9IiIxOT1zV6keEZHGcjrw1waC+IDCgpyupohIi+R0RPQ7SzL7fL5sF0VEpMPI6cBfG9Ba/CIiiXI68PvrgurYFRFJkNOBv9Zfrxa/iEiCnA78NYEgXXW9XRGRODkd+Gv99XQtUuAXEXHL6cC/y19PcZFSPSIibjkd+Gv89ZSoxS8iEidnA384HGaXv56SYgV+ERG3nA38tYEg4TCUFHXJdlFERDqUnA38Nf7IWvxdleMXEYmTs4F/V20k8JcUq8UvIuKWu4HfafGrc1dEJF7uB3517oqIxMnZwF9Tqxa/iEgyORv4d8U6dxX4RUTccjbwb98ZwAd066rALyLilruBf1eA0pIu5OflbBVFRFolZ6PituoAPboVZrsYIiIdTs4G/i3ba+ndvTjbxRAR6XByNvBXba+lXIFfRKSRnAz8Nf56dtbWU95DgV9EJFFOBv4t22sB1OIXEUkirbGOxpgRwEygHKgCplhrlyfskw/cC3wbCAPTrbWPZLa46VlTWQ1Av94l2Xh7EZEOLd0W/4PADGvtCGAG8FCSfc4DhgP7AIcBNxtjhmaikC0RDof5eNlmuhYVMKhvt9399iIiHV6zLX5jTF9gDHCCs2kWcL8xpsJaW+na9WzgD9baEFBpjHkWOAu4I8NljlNXH+LthetYs2Ebm7bUsG5zNUtXf8PJhw/VGH4RkSTSSfUMBtZZa4MA1tqgMWa9s90d+IcAX7nur3b2SVt5eWlLdgfg/cXruf2JeUBkeYYBFd045wTD5BMNeXm+Fr9eZ1NRUZbtImSNV+uuentLe9S7Q61nUFVVTSgUbtFzhvcr49H/OYEd22ooK+mCz+eLvVauq6goo7JyR7aLkRVerbvq7S3N1Tsvz9eqBnM6uZA1wECn8zbaiTvA2e62GtjTdX9Ikn3aRd9eJXTvVhgL+iIiklqzgd9auwlYCEx2Nk0GFiTk9wGeAi4xxuQZYyqA04GnM1lYERFpu3R7P6cBVxhjlgFXOPcxxrxojBnr7PME8CWwHJgL3GKtXZnh8oqISBulleO31i4FxifZfpLrdhC4LHNFExGR9qDxjiIiHqPALyLiMQr8IiIe01HG8ecDbZpw5YXJWsl4td7g3bqr3t7SVL1dj+W35DV94XDLJky1kyOAt7NdCBGRTupI4J10d+4ogb8IGAdsAIJZLouISGeRD/QHPgL86T6powR+ERHZTdS5KyLiMQr8IiIeo8AvIuIxCvwiIh6jwC8i4jEK/CIiHqPALyLiMR1lyYZWM8aMAGYC5UAVMMVauzy7pWodY8ydwPeBocCB1tpPne0p69jaxzoKY0w5kWs5DAMCRK7n8GNrbaUxZgLwENAVWAWc71wYiNY+1tEYY54F9gJCQDVwhbV2YS5/51HGmF8CN+P81j3yfa8Cap1/ANdba1/Z3XXPhRb/g8AMa+0IYAaRD6GzehY4iviL1kPTdWztYx1FGLjdWmustQcCK4Dpxpg84Engcqf8bwHTAVr7WAf1I2vtQdbag4E7gcec7bn8nWOMGQNMwPmte+j7BjjTWjva+fdKNureqQO/MaYvMAaY5WyaBYxxLv3Y6Vhr37HWxl2nuKk6tvax9q5HS1hrt1hr33Rtmkvk2s2HALXW2uj6Iw8CP3But/axDsdau811twcQyvXv3BhTROSg5L5wkye+7xR2e907deAHBgPrnKt/Ra8Ctt7ZniuaqmNrH+uQnBbMZcC/gCG4znystZuBPGNM7zY81iEZYx4xxqwGfgP8iNz/zm8BnrTWrnJt88z3DfzZGLPIGPOAMaYnWah7Zw/8klvuI5Lnvj/bBdmdrLUXW2uHADcCd2S7PO3JGHMYMBZ4INtlyZIjrbUHEVmU0keWfuudPfCvAQYaY/IBnP8HONtzRVN1bO1jHY7Tsb0PcLa1NgSsJpLyiT7eBwhZa7e04bEOzVr7BHAssJbc/c6PBvYDVjodnYOAV4DheOD7jqZyrbV+Ige/iWTht96pA7/Te70QmOxsmgwssNZWZq9UmdVUHVv72O4rfXqMMbcSyVee7vxBAMwHuhpjjnDuTwOeauNjHYoxptQYM9h1/xRgC5Cz37m1drq1doC1dqi1diiRg9y3iJzp5Pr33c0Y08O57QPOIfJ97fbfeqdfltkYsy+R4Wu9gK1Ehq/Z7JaqdYwx9wLfA/oBm4Eqa+3+TdWxtY91FMaY/YFPgWVAjbN5pbX2DGPM4URGpRTTMFTta+d5rXqsIzHG7AE8B3Qjch2KLcC11tqPc/k7d3Na/Sc7wzlz/fveG/gHkTX084HPgJ9Zazfs7rp3+sAvIiIt06lTPSIi0nIK/CIiHqPALyLiMQr8IiIeo8AvIuIxCvwiIh6jwC8i4jEK/CIiHvP/AaqlIRq+6wnGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_cor_ma = ma(result_cor)\n",
    "print(result_cor_ma[-1])\n",
    "plt.plot(range(len(result_cor_ma)),result_cor_ma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test with various correlations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1  0.   0.1  0.2  0.3  0.4\n",
      "  0.5  0.6  0.7  0.8  0.9]\n"
     ]
    }
   ],
   "source": [
    "correlations = np.linspace(-0.9,0.9,19)\n",
    "print(correlations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8218872\n",
      "0.7833964\n",
      "0.7152627\n",
      "0.66930735\n",
      "1.0065683\n",
      "-0.9 : 0.9580456\n",
      "0.54955137\n",
      "0.29476312\n",
      "0.5913655\n",
      "0.6365337\n",
      "0.38067517\n",
      "-0.8 : 0.4846191\n",
      "0.26738563\n",
      "0.15232995\n",
      "0.2236997\n",
      "0.32591072\n",
      "0.22936112\n",
      "-0.7 : 0.31000555\n",
      "0.33736977\n",
      "0.14369842\n",
      "0.17704742\n",
      "0.19388501\n",
      "0.32094625\n",
      "-0.6 : 0.22088282\n",
      "0.15036106\n",
      "0.13677296\n",
      "0.20268154\n",
      "0.14302623\n",
      "0.19971177\n",
      "-0.5 : 0.14044161\n",
      "0.12075566\n",
      "0.11345535\n",
      "0.20858356\n",
      "0.16160753\n",
      "0.11620292\n",
      "-0.4 : 0.12601806\n",
      "-0.010340637\n",
      "-0.042473238\n",
      "0.032113746\n",
      "0.06407347\n",
      "0.041425757\n",
      "-0.29999999999999993 : 0.04813475\n",
      "-6.2100575e-05\n",
      "-2.072574e-05\n",
      "0.00071551604\n",
      "0.0061065704\n",
      "0.003836454\n",
      "-0.19999999999999996 : 0.0052854484\n",
      "-0.00013298911\n",
      "-0.0038910871\n",
      "-0.005217775\n",
      "0.005139473\n",
      "0.006764142\n",
      "-0.09999999999999998 : 0.00851246\n",
      "1.4888283e-06\n",
      "2.078485e-05\n",
      "-0.0003631726\n",
      "-4.619593e-06\n",
      "-7.5127464e-05\n",
      "0.0 : 1.9362599e-06\n",
      "-0.00013056492\n",
      "-4.0744257e-05\n",
      "-5.3294934e-06\n",
      "-1.618464e-06\n",
      "-0.00042317493\n",
      "0.09999999999999998 : 1.4187177e-05\n",
      "-0.0009919407\n",
      "0.01843608\n",
      "0.011063125\n",
      "-0.012622882\n",
      "-0.008004868\n",
      "0.20000000000000007 : 0.025346614\n",
      "-0.0057090297\n",
      "0.07218499\n",
      "0.077516936\n",
      "0.13802114\n",
      "0.07094885\n",
      "0.30000000000000016 : 0.04450101\n",
      "0.04175249\n",
      "0.12077815\n",
      "0.14327744\n",
      "-0.04658608\n",
      "0.06299533\n",
      "0.4 : 0.09087456\n",
      "0.24115951\n",
      "0.11146946\n",
      "0.2108359\n",
      "0.26514512\n",
      "0.15518916\n",
      "0.5000000000000001 : 0.18008022\n",
      "0.18207496\n",
      "0.2039372\n",
      "0.19322066\n",
      "0.19427021\n",
      "-0.028779417\n",
      "0.6 : 0.19631623\n",
      "0.40942466\n",
      "0.37758964\n",
      "0.35871524\n",
      "0.18883121\n",
      "0.31424138\n",
      "0.7000000000000001 : 0.3348583\n",
      "0.5485561\n",
      "0.58335054\n",
      "0.47682956\n",
      "0.2586611\n",
      "0.36256024\n",
      "0.8000000000000002 : 0.4620555\n",
      "0.8277906\n",
      "0.4437629\n",
      "0.54102796\n",
      "0.4580155\n",
      "0.8436885\n",
      "0.9 : 0.74142\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_result = []\n",
    "for rho in correlations:\n",
    "    rho_data = np.random.multivariate_normal( mean=[0,0],\n",
    "                                  cov=[[1,rho],[rho,1]],\n",
    "                                 size = 300)\n",
    "    mine_net = Mine().cuda()\n",
    "    mine_net_optim = optim.Adam(mine_net.parameters(), lr=1e-3)\n",
    "    result = train(rho_data,mine_net,mine_net_optim)\n",
    "    result_ma = ma(result)\n",
    "    final_result.append(result_ma[-1])\n",
    "    print(str(rho) + ' : ' + str(final_result[-1]))\n",
    "    plt.plot(range(len(result_ma)),result_ma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f9b9b1820b8>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j9Xf2cdmZMw5P5x6rVPzHcG71NLLSk1nzeqPTUUTEYT19g9z37FbKCjO47Mwqp+OcMBX/MaSmeLhweQUbtrVq5k6RBPfkS9tp6+jjU5eeRHJS7NdmWN+BMWaeMeY1Y0xt6M+5x9nXGGMOGWN+FLmYzrhgeQWpyR7WvK6xfpFEta2pnRfWNXHB8grmlOc6HSciwv3VdTdwl7V2HnAXcM9oOxljPKHHnopMPGdlpSdz3pJprN2yn9aDPU7HEZEpNjDo57dr3qUgJ5VrzpvldJyIGbP4jTHFwDLgodCmh4BlxhjvKLt/E3gaqI1YQodddGolLhc8+4ambBZJNI88X8se3yE+fvF80lKSnI4TMeEc8VcCzdZaP0Doz92h7YcZYxYDFwM/jXRIJxXkpHHmolJertnNwU4t1CKSKJr2d/H43+o4Y2FJTK2uFY6I/AozxiQD/wl8ylrrN8ZM6PMUFkbnJVIfveQkXt20h6f/sZ2PrTzJ6Thh8XqznY4QFuWMvFjJGs05/YEgP3hwHZnpyXzp+qXkZqU6HSmiwin+XUC5McYTKnUPMC20fVgZMBtYHSr9PMBljMmx1n423DA+XxeBQPRNk5DmhmVzvTz96g7OPbmU9NTofsvn9WbT0tLpdIwxKWfkxUrWaM/51zcaqW08yG03Lae/p5+Wnn6nI43K7XZN6IB5zKEea+1+YAOwKrRpFbDeWtsyYp9Ga22RtbbKWlsF/Az41XhKP9qtPGMG3T0DvLRht9NRRGQStRzs4clXtlM9u5DzlpY7HWdShHtVzy3ArcaYWuDW0N8xxqw2xpwyWeGiyaxpOVTPKeLZNxsZGNSUzSLxKBgMct8zW3G5XHz8oticeTMcYY1ZWGu3AqePsv3SY+z/nROLFZ2uvWAu3/7P13jtnb2cu3ia03FEJML+uXkv7+xs46YV8yjMTXM6zqSJ/VvQptCSeV5mlGaz5vWGqDwXISIT197dz8N/q2NORS7nL4vPIZ5hKv5xcLlcXHbGDPa19bCutmXsJ4hIzHjwuVr6Bvx8auV83HE6xDNMxT9Oy+Z5KclP5y9aqEUkbqyva+HNrfu54qwqygoznY4z6VT84+R2u1h5xgwa9naypaHN6TgicoIO9Q7y+2ctFd5MVp4xw+k4U0LFPwFnLiwlNytFC7WIxIHH/76N9u5+PnXpSSR5EqMSE+O7jLDkJDcXnzqddxva2L67w+k4IjJBtrGNv2/YzYpTKplZluN0nCmj4p+g85ZMIyM1SVM2i8So/gE/v1uzlaLcNK4+J35m3gyHin+C0lOTuGB5BetqW9jj63Y6joiM059e3cm+th4+sXI+qSkep+NMKRX/CbjwlAqSk9ysWavlGUViSXNrN8++0cgHTi5lYVWB03GmnIr/BORkpHBO9TRe27yXAx29TscRkTAEg0EefK6W1GQP150/x+k4jlDxn6CLT6skGIS/vqmFWkRiwdu2hXcb2rj63FnkZKQ4HccRKv4TVJSXzukLinlpw266egacjiMix9E34OeRF+qo8GbywaWJO9+Wij8CVp4xg74BPy+83eR0FBE5jtWvNeDr6OOmFfPwuBO3/hL3O4+gCm8WS+YUsXptA9ua252OIyKj2H+whzVrGzl9QQlmer7TcRyl4o+QT6ycT15mKj9/bCPNLV1OxxGRozz8fB0et4vrE/SE7kgq/gjJzUzhthuXkJTk5iePbqS1vcfpSCISsmm7jw3bWrniA1XkZ8fX+rkToeKPIG9eOrddv4S+fj8/fmQjHd3RuU6nSCIZGAzw4HO1lBRksOKUSqfjRAUVf4RVFGfxleuqaevo5aePbqSnb9DpSCIJ7bm3drGvrYePXjiX5CRVHqj4J8Xcijy+cPUimlq6+MUTNQwM+p2OJJKQ2jr7+POrO1kyp4iTZxU6HSdqqPgnSfXsIj592UlsbTzIPX/agj+gBdpFptqjL27DHwhy44VznY4SVVT8k+jMhaWsunAu62pbuO8ZqxW7RKaQbWxj7ZZ9rDx9OsV56U7HiSpJTgeIdytOqaTz0ABP/3Mn2RkpXPvB2U5HEol7/kCAB56rpTAnlUvPTIxVtcZDxT8Frj5nJl2H+ln9egNZ6clccvp0pyOJxLW/r99NU0s3X7hqEanJiTXlcjhU/FPA5XLxsYsMXb2DPPriNrIzkvnAyWVOxxKJSx2H+vnDy9tZUJXPcuN1Ok5UUvFPEbfbxWcuX8Ch3gF+u3orGWlJLJ2rH0qRSHvypXr6Bvx89MJ5uFwup+NEJZ3cnULJSW6+9JGTmVGazX889Q62sc3pSCJxZceeDl7ZuIcPLa9gWlGm03Gilop/iqWlJPHV66rx5qVx5xM1NO7rdDqSSFwIBIPc/9dasjNTuPLsmU7HiWoqfgdkZ6Rw2w1LSE9N4iePbGBf2yGnI4nEvFc37WHHng6u++Bs0lM1in08Kn6HFOSkcdsNSwgE4ccPb+BgV5/TkURi1qHeAZ74ez1zynM5c1Gp03GinorfQWWFmXzt+sV0HhrgJ49soLtXK3iJTMRT/9hB56EBbloxD7dO6I5Jxe+wmWU5fOmak9l74BA/f7yGvgHN6yMyHk0tXbzwdjPnLS1nRmm203Figoo/CiysKuCzVyykvqmdu57cpEndRMIUDAZ58Lla0lM9fOTcWU7HiRlhnQExxswD7gUKAR9ws7W27qh9/g24EfADA8C3rLXPRjZu/DplfjGfXDmf363Zyp2P1/Cla6p1x6HIGN7cup+tjQf5+EXzyEpPdjpOzAj3iP9u4C5r7TzgLuCeUfZ5AzjVWlsNfBp4xBijmZHG4ZzF0/jUpSexZWcbdz5eQ1+/jvxFjqWv388jL2xjenEW5y0pdzpOTBmz+I0xxcAy4KHQpoeAZcYceS+0tfZZa+3wdYk1gIuhdwgyDmdXl/HfL1/A1sY2fvrYRnr7tZCLyGiefm0nbZ193HTRPNxundAdj3CO+CuBZmutHyD05+7Q9mO5Gai31jadeMTEc+aiUj57xUK2NbXzE63iJfI++9oO8ewbjZy5sJS5FXlOx4k5Eb/LwRhzHvA9YMV4n1tYmBXpOBHn9U7NVQOXn5dNfl4Gd9z/Fnc+uYn//ZkzyRzHGOZU5TxRyhl5sZJ1PDn9/gC79nexbddB6psO8rbdT3KSh1uuXUxBTtokpoyd13M8XGMtDhIa6qkFCq21fmOMh6ETvHOttS1H7Xsm8ChwpbV23ThyVAE7fL4uAoHoXazE682mpWVqp1hYV9vCfzy1mcriLG67cQmZaWOXvxM5J0I5Iy9Wsh4v56A/wO7Wbnbu7aRhXycNezvZtb+LgcGhVexSkz1ML8ni4tOms2ze5E50GO2vp9vtGj5gngnsDPd5Yx7xW2v3G2M2AKuA+0N/rh+l9E8FHgGuHWfpy3Esm+fli1efzL8/tYk7HlrP7Tcu1dULEjcGBgM0t3bRsHeo4Hfu7aSppYtB/9ABYFqKhxkl2Zwfuka/qjSbkvwMjemfoHCHem4B7jXGfBtoY2gMH2PMauDb1tq3gH8H0oF7jDHDz/u4tXZTZCMnniVzi/jSR6r55ZND5X/bjUvIyUhxOpbIhNTuOsjDL9Zjdx6gqaULf+hdfnpqEjNKsrhweSUzSrOZUZpNcX667sSdBGMO9UyRKjTUM6bNO3z84olNFOen840bl5KTOXr5O50zXMoZedGe9d2GNn766EZSUzzMKMliRkn24SN5b1561M2fH+2v56QN9Uj0WDSzkK9eW83PH6/hhw+u4xurlpKXlep0LJGwNOzt5BdP1FCSn84dXzmX3m5NTOgUTdkQY06qKuBr1y/mQEcfP3xwPW2d+scj0W/vgUP85NENZKYl8/UblpCtoUpHqfhjkJmez9euX8zBrj5++MA6DnT0Oh1J5JjaOvv48cMbALjtxiXkZ+tdqtNU/DFqXmUet9+whM6efn7wwDpa23ucjiTyPl097005/rXrF1NakOF0JEHFH9Nml+dy+41LOdQ7yA8fWM/+gyp/iR59/X5+/vhG9rUd4tZrqqkqzXE6koSo+GPczLIcvrFqKb39g/zwgXVaxlGiwqA/wF1PbWL77g4+9+GFnDQj3+lIMoKKPw7MKM3mG6uWMjAY4IcPrGNjXYvm9xHHBIJBfvOXd9m8/QCfuGQ+y02x05HkKLqcM05ML8nmX1Yt5Y6H1/O/7v4nAEW5aVR4syj3ZlLhzaLCm0lJQQZJHv2+l8kRDAZ56Pk61m7ZxzXnzeLcxdOcjiSjUPHHkYriLL7/mTNo6eznnW0tNLV00dTSTU29j0DoRr0kj4vSgkwqit/7ZVDhzSI/OzXqbp6R2PPnf+7kb283cdGplVx6xgyn48gxqPjjTFZ6MjOnFzCzOPPwtoHBAHt83TS3dB/+ZWAbD/L6O/sO75ORmnTEO4NlppjcY9wZLDKaF9c18dQrOzhrUSnXXzBHBxJRTMWfAJKT3EwvyWZ6yZHTy3b3Dhzxy6CppYvXt+ylp8/P6tcbuH3VUkrydfmdjO2Nd/dx/19rWTy7kE+unK/5daKcij+BZaYlM68yj3mV7y1kEQwG2b67g58/XsMP7l/HbTcuocIb/eskiHM27/Dxqz9vYU5FLp+/apHOIcUA/R+SI7hcLmaX5/I/bloGLvjhA+vYubfD6VgSpep3t3PXk5spK8zkK9dWk5LscTqShEHFL6MqL8rkX29aRlpKEnc8tJ7aXQedjiRRZndrNz97dCM5mcl8/YbFZISxSJBEBxW/HFNxfgb/+rFl5Gam8pNHN/DOjgNOR5Io4Wvv5cePbMDjcXPbDUs0S2yMUfHLcRXkpPHNm5ZRnJfBzx/fyPralrGfJHGt41A/P35kA739fr5+/WKKdQFAzFHxy5hyMlP4l48upbI4m7v+sJnXt+x1OpI4pKdvkJ89uhFfRy9fubb6fVeKSWxQ8UtYstKTuf3GJcyrzOVXf9rCyxt3Ox1JplAwGKSmvpX/c99bNO7r4vNXLjriajCJLbqcU8KWnprEV69bzF1/2Mzv1mylt9/PRadWOh1LJllTSxePvLCNd3YcoDg/na9cV83JswqdjiUnQMUv45KS7OHWa07mnj+9w8N/q6Ovf5DLz6rSXZpxqKO7n6de2c5LG3eTnpLEjR+aywXLynWdfhxQ8cu4JXnc3HLlQn67eit/eGUHvf1+rv3gbJV/nBgYDPD8W7t4+rWd9PUHuGBZBVeePZOsdF2uGS9U/DIhHrebT192EqkpHtasbaS3389NF83TrfoxLBgM8rZt4dEXt9Ha3kv17EJuuGAOZYWZYz9ZYoqKXybM7XLxsRXzSEseKv++AT+funQ+HreGAmLNjj0dPPK3Omqb2in3ZnLbDUtYOLPA6VgySVT8ckJcLhfXfnA2aalJ/OHl7fQN+PnchxdqHDhGHOjo5cmXt/PPzXvJyUjm5ksM51SX6Zd3nFPxywlzuVxccVYVqckeHv5bHb94YhNfvHqR5m2JYn39ftasbeCZtY0EgkFWnjGdy8+sIj1VlZAI9H9ZIuaiUytJS/Fw75qt/PTRjdx6TTUZafoRiyaBYJDXNu/lyZe309bZx6nzi7n2g7Px5qU7HU2mkP5VSkSdu3gaKclufv3nd/nmPa9x2ZkzOH9puY7+HRQMBtl/sIe6Xe28sK6JnXs7mVmWzS1XLmRuhW7CSkQqfom4MxaUUlqQwRMvbeeRF7bx1zd3ccUHqjj75DKN/U+BQX+AXfu7qNt1kLqmduqa2+no7gegICeVz1y+gNMXlugKrASm4pdJUVWaw203LGFrQxtPvryd+56xPPN6I1edM5PTFqh0Iqmnb5D63e3U7WqnYX8XWxsO0D8QAKAoN42FVQXMrcxlbnkuZUWZeu1FxS+Ta/6MfP71Y8uoqffx5Mvb+c8/b+EvrzfwkXNmsaJIK3tNRFtnH3VNoaP5poPs2t9FMAguF8wqz+Wc6mnMrchlbkUe+dmaLlneT8Uvk87lcrF4ThEnzy7kra37+cPL2/nFk5t49q1dfPisKhZU6Xrx4+nuHaBmm4/NO3zUNbXT2t4LQEqym9nTcrnirCrmVuQxa1oO0yvyaWnpdDixRDsVv0wZt8vFaSeVsNx4+eemvfz5tQZ+9PAGTpqRz0fOncUwJc7nAAAJy0lEQVTs8lynI0aN1vYe1te1sr62hdpd7QSCQXIykplbmceFp1QytyKXyuIsnTORCVHxy5TzuN2cs3gal583h8eft/zlnzv5/u/fZsmcIq4+dxaVxYk3BBQMBmnc18X6uhbW17Wya38XANOKMll5xnSWzC1iZlmOxuclIsIqfmPMPOBeoBDwATdba+uO2scD3AlcAgSBH1hrfx3ZuBJPUpI9rDilknOqy3j+rSbWrG3kO//1BqctKOGqs2dSUjDxlZ0CgSB9A34G/QEy0pKi8k7UQX8Au+sgG2pbWb+thQMdfbhcMKc8l+vPn8PSuUUn9BqIHEu4R/x3A3dZa+83xnwMuAe44Kh9bgLmAHMZ+gWx3hjzvLV2Z6TCSnxKS0ni8rOqOH9ZOc+sbeS5t3bx5rv7OevkUsoKM+gfCNA34Kd/wE//QID+Qf9720Z+POLxQX/w8Od3uSA3M4W8rFTys1PJy0olLzuV/KxU8rJTyA9tT09NmvQZRnv6Btm03cf6ulZq6n309A2SkuRm4cwCrjx7JovnFJGTkTKpGUTGLH5jTDGwDFgR2vQQ8EtjjNdaO3IB1huAX1lrA0CLMeYp4DrgjghnljiVmZbMNefN5sLlFfzltQb+vqH5cIGnJLlJSfaQkuwmJSn0Z7KHtGQPORkppB7x2Hsfezwuug4N0NbVx8HOPloO9lC76yDdvYPv+/opSW7yQr8Y8od/MWSlUFGWS1dX7wl9b52HBti4rZV3G9rwB4JkZySz3HhZOreIBVUFpOoGN5lC4RzxVwLN1lo/gLXWb4zZHdo+svinAw0j/t4Y2idshYXRP7br9cbGGqOxnNPrzeYrM4u45bolBINBUpI8uN2RPRLvG/DT1tGLr72XA+29+Dp6RnzcS8O+TtbXttA/GIjY15xWlMmHz53N6QtLmV9VgCfC39OwWP5/H41iJed4RNXJXZ+vi0AgOPaODvF6s2PiUjnlDI8HKM5OoTg7Bch53+PBYJDu3kGSUpPxHeg+oa+VmuSmMDft8FDSAV/XCX2+Y3H6NQ2XckaG2+2a0AFzOMW/Cyg3xnhCR/seYFpo+0iNwAzgzdDfj34HIBJTXC4XWenJeL3ZpEXfuWGRCRvzx9laux/YAKwKbVoFrD9qfB/gMeAzxhi3McYLXAU8HsmwIiJy4sI9jrkFuNUYUwvcGvo7xpjVxphTQvv8HtgO1AGvA9+11u6IcF4RETlBYY3xW2u3AqePsv3SER/7gc9HLpqIiEwGjVyKiCQYFb+ISIJR8YuIJJhouY7fA0T8Jp3JEAsZQTkjLVZyQuxkVc4TNyLbuG79dgWDUXHD1NnAK06HEBGJUecA/wh352gp/lTgVGAP4Hc4i4hIrPAAZQzdONsX7pOipfhFRGSK6OSuiEiCUfGLiCQYFb+ISIJR8YuIJBgVv4hIglHxi4gkGBW/iEiCiZYpG6KCMSYD+C2wHBgEbrfWPj3Kfl8GPj1i0yzg19barxtjPgisBmpDj/VZa983pfUU5TxuFmPMvwGfDP31d9ba70Uy5zizXgl8m6Gb+VzAf1lrfxx67JPAz4Cdod13WGuvjkC2ecC9QCHgA2621tYdtY8HuBO4BAgCP7DW/nqsxyIpzJz/BtzI0A2QA8C3rLXPhh77HXAh0Bra/TFr7fcjnXMcWb8DfAHYHdr0qrX2i6HHwvp5maKc9wHVIzZVA1dZa/90vO8hFqj4j3Q70GGtnWOMmQu8YoyZY609YoFUa+2dDP2DxxiTDDQDD47YZYu19hQmT1g5j5fFGHMucB2wKLRprTHmJWvtyw5l3QtcYa3dbYzJBd42xrxhrR2eyuN5a+21Ec52N3CXtfZ+Y8zHgHuAC47a5yZgDjCXoZJYb4x53lq7c4zHpjrnG8CPrbWHjDGLgZeMMWXW2p7Q4z+w1v4ywrkmmhXgPmvt7aNsH8/P9qTmtNbePPxx6DV9AXg2jO8h6mmo50g3MPQDQOi3/1vAyjGecwWwx1r71iRnG2kiOUf7HPdZa3tC5XBfaFukhZXVWrvWWrs79HE78C5DazhPCmNMMbAMeCi06SFgWWjZ0JFuAH5lrQ2Elht9iqFfmGM9NqU5rbXPWmsPhf5aw9C7psJIZhnLOF7T44nEz/Zk5PxvwAPW2rCnRYhmKv4jHb1AfCNQOcZzPs3QW9OR5hlj1hlj1hpjPhHJgCHjyXmsLBP5Xidi3F/HGDMfOIOhI6xh5xljNhhjXjbGXBaBXJVAc2jluOEV5HaPku14+afiNQw350g3A/XW2qYR275ujNlkjHnKGHNShDNOJOuNxpgaY8xfjTFnjtgeda+pMSYF+CjwX0c9dKzvIeol1FCPMWYdQz9YoymZwOcrY+jt4SdHbF4HVFpr240xM4HnjTHN1trnHch5wlnGMkmv6R+BLwy/AwCeBh6x1vYYY5YCa4wx51tr351Q6DhmjDkP+B6wYsTm/8nQu9KAMeZm4BljzKzh4nPA3cD3rbUDxpgVwB+NMSdZa30O5RnLVUCjtXbDiG2x9j0cIaGK31q77HiPG2MaGRpeaAltmg68eJynfAJYba0dPmmGtbZjxMc7jDFPAR8Awi7bSOUcI8vw5xg2HdgVbsZIZw3tWxzK9v+stY+N+BojX9/1xphXgdMYGg6aqF1AuTHGY631h07UTuP9r8Fw/jdH5G8I47FICTcnoaPO+4ErrbV2eLu1tnnEx/cZY34KVDiV1Vq7d8THzxljdjF0rukl3ntNw/03OGk5R/g0Rx3tj/E9RD0N9RzpMeBzAKETS6cCzxxn/09x1A+EMabMGOMKfVwAXARsGOW5k55zjCyPATcbY9KNMekMDQ88GuGc48laCDwH/NJa+5ujHisf8fEMhoaBak4klLV2P0OvxarQplXA+tBY/dH5P2OMcYfGgK8CHg/jsYgIN6cx5lTgEeBaa+26ox4b+fpdzNCVP81E2DiyjsyzBKgChn9Rjfff4KTlDGWoYGiu+wfG8T1EvYQ64g/DHcDvjDHbGPrH8VlrbSeAMea7wG5r7d2hv38AyOLIs/wA1wCfN8YMMPT63mut/aNDOY+ZxVr7d2PMk8A7oc95n7V2Mo5Wws36TWAe8DljzOdCz/25tfa3wBfN0OWeg6Ht37LWro9AtluAe40x3wbaGPrlhzFmNfDt0An73wOnA8OX+n3XWrsj9PHxHoukcHL+O5AO3GOMGX7ex621m0LPLQECQAfwYWvtIJMjnKz/1xiznKGfh/5QzuEj6GP+vDiQE4be1f/ZWtt21POP9z1EPc3HLyKSYDTUIyKSYFT8IiIJRsUvIpJgVPwiIglGxS8ikmBU/CIiCUbFLyKSYFT8IiIJ5v8DxuRUp74Uz64AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(correlations, final_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equitability experiment\n",
    "\n",
    "Check more information at [original equitability paper](http://www.pnas.org/content/pnas/111/9/3354.full.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Make toy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(low=-1.,high=1.,size=3000)\n",
    "f1 = x\n",
    "f2 = 2*x\n",
    "f3 = np.sin(x)\n",
    "f4 = x**3\n",
    "eps = np.random.normal(size=3000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9b9b089048>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x, f1,color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9b9a06ad30>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hrc3UcXYcHz090lqYqWSFtBBiUlzXobPT5uhRiz/9ySKdhuPHTRIYawfVd73LQ6kU0eggPvnrM6NV3WwlIURlOU6Y/v7sKmfr9CrnHTvg9783SWH9+twOqsuWQSjkMX9+mmQyRjQqaxaqgSQHIcSEZLfVPn7cAkaX7Fy9Gnbvhttuy22U19oKzc0etj3M0FCsovGL4kjDTggxLjPg7NLR4eOKKywOHy484DwwAN/9Lrz1rXDeeR5tbcOkUlFJDFVIWg5CiDEFgwEsK0QkAvmthbEGnB0HgkHw+z3q6hIMDSUqFbqYImk5CCEKcl2HoaEQ+/ZZrFxpxhbOVrJz+3YIBEwdZ8eJEo9LYqhm0nIQQowQCgVJpYKcPGmK8KxZM7q1kF+yc8kScByPYBBqa5NEo7LCeTaQloMQ4jTXdejrC9Lba5FMWiSTY7cWOjtNNxJ4LFiQwu+XrS9mE2k5CCEIh0NEo4FR01N37y7cWlAKbNsjFIKamgTRqHQhzTbSchBijnNdhzfeCNDba51ODGASwm23mfUL+a2F1lZTma252bQWZGxhdpKWgxBzlOs69PTY9PVBKGQRj4+envrEE6Yoz65dphBPMOjR0AAQIxqV/ZBmM2k5CDEHua7Dq69mK7NZXHGFKbZz220jr2tvN2U7QyEIh01rIZmUjfLmAkkOQswh2ZKdkYjNmjUju5DWrDHlO/Onp27dakp21tV5NDQkZFvtOUS6lYSYA2zbRzDonJ6FNFZltmQyt/XFwoVmT6SamiSxWJy4TESaU6TlIMQsF4tBPG62vjDdSHDFFYUrsw0Pw1e+Aq7r0dDgEQ7HZHrqHFWyloNSajmwDWgCeoAbtNb7zrjm68AG4M3Mod9prb9YqhiEEDnBYAAI8cor0NlpsWHD6MpsDzwAH/+4SQyPPQbz53s89xzMny8b5c11pexW+gHwfa31z5RSnwEeBP6qwHUPa61vK3BcCFEi2SI8YMp1bttWeKO85ctBa7MfUk2Nh+umiEaHGJKhhTmvJN1KSqkW4BLgkcyhR4BLMnWihRBlEgj4cd1aXn3V5vLLLWKxkVtf5GtvB88zi9nmzfMIBuMy4CxOK9WYwyLgjUwZ0Gw50Dczx8/0SaXUS0qpXyul3lei+wsx57mug2WF6e62iMUs7r3XHB+rMtvOnWYxW1tbiuHhARKJZOWCFzOO5XnelL+IUurdmO6it+YdewX4jNb6xbxjbUCP1jqplLoK+Dlwsda6ZwK3OR84OOVghZhlhoehqwvicdMS+OpXzeK17DiCZZlCPG1tsGkTXHih6UZqaTHrF/wyZ3GuuAB4faIXl+rX4ghwnlLK1lqnlFI2cG7m+Gla6868x79RSh0B3gY8O9Eb9fQMkE5PLqE1N9cRifRP6rnTSeIqjsSV47oOHR32iP2Qtm0z21zs2WPWLvzP/wm/+Y1ZzGbbZnpqfb0ZW4hGyxruCPJzLM5k4/L5LJqaaot/XtHPKEBrfRzYC3wqc+hTwB+11pH865RS5+U9fiemNaBLEYMQc0kg4CcYrKWz0x61H9KNN8Jdd+U+T6Wgrw/q6jyamz0cJyZjC2JcpWxQfgHYppTaBJwAbgBQSu0CNmmtXwC+kemCSgEJ4Pr81oQQYnyu63DqlM3QkEVnZ+FZSAsXmsft7ebx/Pketp2SpCAmrGTJQWv9KnBpgeMfy3t8Y6nuJ8RcEwoFse0gr74KXV0W8+bB8eOFy3XadnbQ2aOx0SKZjBKPpysXvKg6skJaiCrgug6Dg8HTM5GWLoVEwowvFCrXWVMDzz3nsXx5iro6SKUkMYjiyDwFIWawQMBPOh2mpwcikVzJzvZ2+OlP4c47zfhCdj+kBQtMHeeaGvD5TBGempq6Sn8bogpJy0GIGcp1HYaGwvT1WaTTucQA5uP118PAAHzxi3DxxXDeeR719R6trWZbbSnCI6ZCkoMQM0w4HMLnq+XIEZtXX7VYudIkg0IDz62tcP75ZuuLbGU2GXQWpSDdSkLMELbtIxRy6O4222p7Hnz3uyO3vzhz4NlxTGU2v19mIonSkpaDEDOA6zp4nktnp4+jRy3+9Ce44w649VazrXbh7S88FixIkUhIa0GUnrQchKigYDCAbYfo6YF43GLfPti82axwfughuP9+uP12s/3Fxo1mi22lPEIhmD9fWgti+kjLQYgKcV2HRCKE1hYrVlgsX27KdG7ZYvZBWr/erHZuaTHXd3ZCW5vZKC8UktaCmF7SchCizBwnzMCAn44OCIdHz0Jav95MTV29Oleuc/9+j0AAGhuHiUalCI+YftJyEKKMXNdh/34/L75osWqVqeVcaBZSY6MZV2hrg2DQtBYcZ0Cqs4mykeQgRBk4Tph43GyU9+abFq2tuU3xChXhGRyEHTs82to8amuT0oUkyk6SgxDTzHUdurr8HDpk8dJLFv/wD5BOw9VXwz33wKOPjpyFtGOHx7ve5aFUimh0gFgsXtlvQMxJMuYgxDTJbpSnNaxenau38NBDZtD57rvhwx821z75JAQCZuuLBQsqX2tBCEkOQpSYbfuIxVwGBkyhlc2bCw84nzhhpqYuXWoqsgWDuSI8QlSaJAchSsh1HY4csTlwwKKmxowd/P3f5yqzgUkQLS1msDk74FxTA54XIxodruw3IESGjDkIUQK27WNwELq7bSzLAszitQ0bTIL45jdz17a3mz2RBgfB8zzq64dJJAZIJiUxiJmjZC0HpdRyYBvQBPQAN2it951xjQ3cB3wE8IBvaa1/VKoYhKgEU2vB5sQJ6Oy0OH7c1FnYssWsal63ztRwhuyAs6nMBmBZUYaGpNaCmHlK2a30A+D7WuufKaU+AzwI/NUZ13waWAoswySRPyqldmutXy9hHEKURSDgZ2gozJEj0N9vsXYtIwad87e+8PlAa9OF1NQEljUsaxbEjFaSbiWlVAtwCfBI5tAjwCVKqeYzLr0O+KHWOq21jgCPA2tLEYMQ5eS6Dq+9FuaPf7Q4cCCXGCA36HzjjbnFbIEAhEJmW+1YTBaziZmvVGMOi4A3tNYpgMzHNzPH8y0G8teDHi5wjRAzVjAYOL2YravLLGarqSm8yrmlxYwrPP64R02NR2OjLGYT1aPqZis1NdVO6fnNzTOzZKLEVZxKxBWLwV/+AqtW5bqPHn3UnCtUa6GtDS64ABobLcJhgCB1dcGyxw3ycyyWxFW65HAEOE8pZWutU5mB53Mzx/MdBtqB/8h8fmZLYlw9PQOk096kgmxuriMS6Z/Uc6eTxFWccsdl2z78fpcTJyAatbj3XrOAbc8euPZaePZZ2LrVDDxnk8bOnaYITyg0TH9/jP4KvozycyzObIvL57Mm9aa6JMlBa31cKbUX+BTws8zHP2bGFfJtB25SSu3ADEhfA3ygFDEIMR1c16Gvz+b11y1Wrx454Lxxo0kQsRjU18Mzz5i9koJBj8ZGs5htSHqRRJUq5TqHLwC3KqU6gFszn6OU2qWUek/mmp8CB4B9wB+AzVrrgyWMQYiScJwwqVQtkYjN4KCVqaVgzmUHnG+/3SSKUMgMPNu2qbdQVxeTsQVR9Uo25qC1fhW4tMDxj+U9TgG3lOqeQkwH13U4ftymu3v09NRsayE74Lx1KwSDYFke8+db9PcPVDp8IUpCVkgLkeG6Dn5/LSdP2qRShaen3n67+by93bQWWls9HMcjFIpmBp2FmB2qbraSENPBdR1OnbLp7DRdSPPmnb0Iz44dZsBZNsoTs5W0HMScFgj4CYVq6eiw2bvXDDrX1MDx44WL8LS3w9NPm1oLfr/UcRazlyQHMWeZ1kKY3l5TsjO7mK231+yN9NBDI4vw7NwJDQ0eLS3SWhCzn3QriTknEPATj4eJRCAWs/D7zUyk3l6TBO6+22yad//9pu6C2V7bo7nZY3h4iGhUNsoTs5+0HMScYds+LKuGzs4wr7xisXKlxcUXwwc/CN/+Nvzyl6a10NlpZiXdfDO87W1wwQUeLS1J4vFBUilJDGJukJaDmBNc16G31yaRsHCc3GpmMB+vv95UZdu40XxctsxslNfUlCYejxGLSVIQc4skBzGrOU4Yz/PT0QGrVpk6zs8/X3gm0pIl8LOfAZhttQOBYaJR2T1VzE3SrSRmLdd1SCb9pwecswlhrJlIfj/U13ucc06K4WHZVlvMbZIcxKxj277TeyIdPGgRi41sKdx9d6GZSB5NTR41NTITSQiQ5CBmGdd16O936ez0k0hYPPKI2Qwvv6WwZ4+ZifTkk7B/Pzz3nMfy5aa1IIlBCEOSg5gVQqEgUMurr9pcfrnF0qVw+eVw3XXw7/9u6jbntxS+/GXwPI/WVo/6+rgkBSHOIAPSouq5rkNHh004bLFmzchZSNdeC7t2wT33wO7dYFlm99RQyJOtL4Q4C2k5iKplxhbMttrRqEUgUHgWkt8PP/6xWc9w6pRHfb2H48i22kKcjbQcRNVJpyEQqKGvz+LECbPCua4OPK9wuc5QyIwt+P0eTU3DDA3FSKUqF78Q1UBaDqKqhMMhTp2C117zsWJFbmwhkTAthMceGzm28OijkE57NDZ6zJsXk+mpQkzQlFsOSikX2Aq8GxgGbtNa/7LAdSuBXUBH5lBcaz2qOJAQhdi2j1AoRE+PjedRcGzhySchmcyV6/T7wXFkeqoQk1GKbqXbgD6t9VKl1DLgOaXUUq11oZJYr2it31PguBBjcl2HEydsenos9u0DpQqPLfh8nO4uqqvzSKfBcZJEo/HyBy1ElStFt9J1wIMAWut9wAvAR0vwdcUcFwwGsG1Ta+GyyyyWL4cNG8y5Qiuc02mze2pDg0coFMe2B4jFJDEIMRmlaDksBvLfxx0GFo1x7XKl1ItAEnhAa72t2Js1NdUWH2Ge5ua6KT1/ukhcI8Vi0N0N8TisWjWyC+mrXzXrFlavztV3fvRRCIfhnHOsTLnOcOZfecnPsTgSV3HKGde4ySHzx3zxGKdbi7jXi8AirfUppdQFwG6l1Bta691FfA16egZIp71innJac3MdkUj/pJ47nSSunGAwwMBAiHgcfD5TsvPMLqQnnoBvfCN/bMHDcSAcTtDfn6C/Qi+l/ByLI3EVZ7Jx+XzWpN5Uj5sctNaXnO28Uuow0A5EMocWA08X+Dp9eY8PKqUeB94PFJUcxOyVXcyWv3tqdpO8M6envv46OI7pRmprMwPOcelBEqJkSjHmsB34PEBmQPq9wL+deZFS6hyllJV53Ah8CNhbgvuLKhcMBvD7c4vZ7r0XLr3UJIZC5Tp37ID/9J88LrrIY9GiYZmJJMQ0KMWYw7eBnyil9gMp4GatdT+AUmoz8KbW+gfAGuAWpVQyc99tWusnSnB/UcVc1yEatTl61Do9ttDebhLCL34Bt946slznggUQDEJDg2ktDEleEGJaTDk5aK0HgbVjnNuU9/h7wPemej8xO4TDISBATw+k09aoQef1601CuP9+s8W250E4bMYWGhstTp6UrCDEdJIV0qLsXNdheDhAV5fFkSMWiQS0tY285tAh01L42tfAdc1itubmFD7fAIFAZeIWYi6RvZVE2ZitLwKZaaoju5G2boU77jC1FsAcO+88cF2zmC0cjhGNDlf2GxBiDpGWg5h22d1T9+8PcNllFi+8MLobad062JTphDSV2cC2zdYXtj1AMimJQYhykpaDmFau63DypE1fXy4hNDYW3v5iyRL4y18gEPBobASfL040mqxM4ELMcdJyENMiFAoSDputL97/frNuIZsQensLb38RCJitL9raTMnOREISgxCVIslBlJzrOvT1Benqsk4vaMtPCHffPXrtws6dJinYttRxFmImkOQgSsa2fYTDtfT02MTjpgjP1q1mQVt+Qtizx0xR3b0b9u/3+N3vPJYtk8VsQswkkhxESbiug9/vsm+fdboIz8qV5tx995mPGzfCAw+YcYW77zYDzm1tKYLBASnCI8QMI8lBTEl2JlJvr01vr3V6p1TIzULq7obbb4fOTrOeoa7OY/58j6amhLQWhJihZLaSmDTHCdPf76evz2I4M9O00CykmhpYuhSeesokhmxlNtkoT4iZS5KDKFog4MfzwkQikEhYdHebTfIaGwvvoDo4CKGQR329TE8VolpIt5IoiuvapiIvAAAUPklEQVQ6pFJhBgYsurstPvxhuOwy+MpXzBbav/jFyFlIW7fCkiUejY1JmZ4qRBWRloOYkGAwQDweIhKBVMrCtmHt2pHjC3/zNyYZZIvw2Ha2CE+cWEySghDVRFoOYlyu63DsWIiXX7ZYudLMRHrjjcLjC8GgeRwM5jbKk9aCENVHkoMYUywG0ahZt3DggMW6dbmEkK3Qlq+93VRma2ryqKuLyUwkIarYlJODUuozSqmXlFLDSqn/Ms61Nyml9iulXlNKfU8pJclphnJdh1degcsvtxgctKipGdlSGGuVc2vrMLGYbJQnRLUrxZjDXuCTwN+d7SKl1AXA14B3AT3Ak8BngIdLEIMoEccJMzjop7sbhoZMwZ1AwMw4yp+JlF3lbMYXPMJhqKtLMDSUqGj8QojSmPI7d631n7XWrwDpcS69Fnhcax3RWqeBHwLXTfX+ojQCAT+JRC1dXX76+y2+/GXr9CykeNwsXtu6dWRL4WtfM2ML2VXO8bgkBiFmi3LOVloM5A9hHgYWlfH+Ygyu69DRYZ/eJC9bw7mz07QQPv5xePppiEbh17+GdNqsW2hqguHhKNHoeO8LhBDVZtzkoJR6EfOHvZBWrXWqtCGdXVNT7ZSe39xcV6JISqsSccXjZmuLwUHGrOGc3Q6juxvOOQcsC/x+aGmxCIcBasoeN8jPsVgSV3EkrgkkB631JSW612Egf37LYuBIsV+kp2eAdNqbVADNzXVEIv2Teu50qkRcruvQ2WnT2WnR3Gy6jfIHnLNFecC0JFpaoL7eIxg0W1/090N/hV5K+TkWR+IqzmyLy+ezJvWmupyzhR4DrlFKNWdmKd0E/FMZ7y8wi9lc1xThufJKM67woQ/BN79pttbOam/P1WDYscNjwQIP25aN8oSYK0oxlfVTSqmjwFrgLqXUUaXUWzLnNiulvgCgtT4A3AX8AdgHHAB+NtX7i4lzXYf+/hCRSK4IDxSu4bx9O1xyCfz2tx5KpYhGZcBZiLlkygPSWutHgEfGOLfpjM8fBB6c6j1FccLhENFogI4OWLXKYtu2s9dwdhzw+z0sy2LevJS0FoSYg2QR2iznug779gX4X/+rcMnOrPZ2M9icTkNtrUdDQ4pzz0USgxBzlCSHWSoUCuJ5tXR326xePXKFc+HVzdDQ4NHensayopIUhJjjZFfWWca2ffj9LidOQDJp6jhfeWWutXDokFm7kC3ZuWSJ6UZynFwRHiGEkJbDLOK6Dj6fy/79FpdfbrFsmanjfMst8PLLsG1brrXQ2WmSQjrt0djoEQ7LTCQhRI60HGYJ13Xo6bFJJq3TtZoPHTL/rr0WnnzSzEjatg0WLjS1FkIhqK1NEotJvU4hxEjScqhypjJbLVrbrFhhai1s2ABbtuTWLRw6ZDbPu+ceOP9804XU3JzC7x+QxCCEKEiSQ5XKX8z24osWq1dbo7a/uP1283l7OySTEA6bmUgyPVUIMR5JDlXIdR2i0RDd3WZ66pm1FiC3/YVZ4QwLFshMJCHExMmYQxWxbR+W5dLZCb29FokEI9Yt5CeI9nY491x46imPtjZIJmMkk8OkyrpNohCiWknLoUq4rkMi4dLfb+F5FpGI2UK7vX3sdQuOY2otRKNSmU0IURxpOcxwwWCAeDzEkSPQ32+xdi2nay780z/Bz38On/50bt3ChReaAjzz50MgIGMLQojJkeQwg7muw/HjNmARCsFHPjKy5sLf/I2pzvbDH8KiRWbAORjMDTgnkxUNXwhRxaRbaQYKh0O4bi09PTbDwxZ/+YsZVyg06OzzwU03wdCQR3Ozh+vGpLUghJgySQ4zjOs6DA0F6OiwWLHCYvlys24hnYarrx55bf6g8/LlMrYghCgd6VaaIUKhILYd5MgRsCxrVNnOtWvhV7+CvXtzYw47dnjU1YHjxIlGpQ9JCFE6khxmgFgMkskgkYjFgQMwb17hLqQTJ8ygs1IQCHg0Ng4zNBQjITV4hBAlNuXkoJT6DPDfgLcAf6u1/t4Y160EdgEdmUNxrfWlha6dK1zXYXDQpqsLhoctfD5obYXDhwuvW+jthdZWjwULwPNiDA1JF5IQYnqUouWwF/gk8HcTuPYVrfV7SnDPqmbbPgIBl0gEEgmL/fth82azU+r27fD735t1C+vX57qQdu6EtjaP+nqZniqEmH6lKBP6ZwClVHrq4cx+4XCIoaEAhw7lxhXa200y2LgxN7Zw++1w773Q0mKSQltbing8TjQqL7MQYvqVe8xhuVLqRSAJPKC13lbm+1eMbfuwbYejRy18vtEDzuvXm2SwejX4/fDtb5tpqqYIjww4CyHKa9zkkPljvniM061a64nu1vMisEhrfUopdQGwWyn1htZ69wSfD0BTU20xl4/S3Fw3pedPRixmxguSSVOn2efL1VvIyt8oz7bNsbY2cBwLny8MhMseN1Tm9ZoIias4EldxJK4JJAet9SWluJHWui/v8UGl1OPA+4GikkNPzwDptDepGJqb64hE+if13MmwbR/BoMupU9DVZbF6da4baetWuOMOU7ITzLHBQXjsMTM91bZjRKPDRKNlC3eUcr9eEyVxFUfiKs5si8vnsyb1prpsi+CUUucopazM40bgQ5jB7FnJdR2SSZfubotkMpcYwHxctw42bTKfZ7fVfuc7PS66KEU6LYvZhBCVNeXkoJT6lFLqKLAWuEspdVQp9ZbMuc1KqS9kLl0D/FkptRf4LfCw1vqJqd5/JnJdh95em6NHLVauzJXrzHfoEFxwATz/PDz1FFx4oUddXVJmIgkhZoRSzFZ6BHhkjHOb8h5/Dyi4BmK2cJwwp075OXnSrFu4666z11twHFi0yKOlxaK/f6BygQshxBlkb6UScF0Hn6+Wffv8vP/9FsuXW3z0o3DrraaOc+F6Cx7z53vMmxcnXJmxZiGEGJNsnzFF2W21U6mzT0/N1ltQCkIhj/nz8xezSXYQQswskhwmybZ9hEIhIhFTb6Grq/C4QkuLedzZmV3MBsPDsm5BCDGzSbdSkcz01Bp8Phet/axcaXH4MBw/nus2ympvN2sXOjrguec8lDLbaicSkhiEEDObJIciOE4Yv9/l5EkfJ0/mpqf29sK2baPHFXbsgNpaj5YWj7o6KcIjhKge0q00AYGAn3Q6TH8/HDtmksK2bblupLvvhi1b4P77R+6HVF8Prisb5Qkhqo+0HMbhug6eF6avz2Jw0MJx4Morc9NTwaxy3rgRbr4Z3vEOMz21rS0FDEhiEEJUJUkOYwgGAySTtfT12Rw4YBazLVsGH/0o3HILvPzyyG6k7IBza6tHQ0NCkoIQoqpJt1IBruuwb5/NNddY7NoFa9aMnKJ67bWwaxd87nO56am27dHcLF1IQojZQZJDHjM9NUx3t4/BQYt77zXbZxeaomrbudZCYyMEg5IYhBCzhySHDNd1SKVsXn3VOt1SaG+Hp58uvPVFOAzPPuuxYIFJCsOyT54QYhaZ82MOrusQDNYSidhEIhauawacwSSEBx6Axx4bOUX1scc8Gho85s2T6alCiNlpTrccXNchFrN5/fWRrYVHHzXnf/xj+M53zDYYTz8N6bRHIABNTdKFJISY3eZkyyEUChIK1XL8uM3AgFVwwPmrXzWfZ3dPDYXM9FTHkempQojZb84lB9d1GBgIsn+/xRVXWMRiYw84my4kaGz0mDdPWgtCiLljznQrhcMh3nwTolEbvz+39UUqNd6AMySTMWIxGXEWQswdU04OSqnvA1cCcWAA+LLW+oUxrr0T+Gzm059ore+a6v0nwnUdjhyxOXAAamosWltzyeCee8wYw7XX5sYcHnvMrFuYNy9JNBovR4hCCDGjlKLl8CTwt1rrpFLqr4F/BC488yKl1ApMKdG3ZQ7tUUo9q7X+bQliGJPrOvT02Bw7ZrFhg0kA//qvudbCj3+c+SaehEAA/H6PefPA86LEYunpDE0IIWasKY85aK1/qbXO7kH978BCpVShr3sdpm70kNZ6CHg4c2xadXfbxOMW69blWgubN8PWrbnpqU89BUNDHnV1Ho2NCYaHB0ilJDEIIeauUo85/BfgX7XWhf6yLgaeyfv8MLCi2Bs0NdUWdf1rr8Hw8MgxhT174I47stNTTYuhpcXKlOsMZf6VV3NzXdnvORESV3EkruJIXMUpZ1zjJgel1IuYP+yFtGqtU5nrPgn8ZybxB78YPT0DpNPehK/3+2s5etQaNejc2Qlgtr7w+eL09yfp7y95uBPS3FxHJFKhm5+FxFUcias4EldxJhuXz2cV/aYaJpActNaXjHeNUmoVsAW4UmvdNcZlh4H8WmmLgSMTCXIqFixIMTho89OfWlx/fW7QeedOj5YWmZ4qhBCFlGK20l8D/wO4Smv9+lku3Q7cl5ndBHADcOtU7z+eaHSI9naHhgabZ56xSKU8gkFoaJCZSEIIMZZSjDlsBRLAo0qp7LErtdY9SqkfAf+stf5nrfUzSqkdwMuZax7WWj9bgvuPKxodIhCAc8+tIxIZACAWK8edhRCiOk05OWitm89y7v864/OvA1+f6j2FEEJMrzm3fYYQQojxSXIQQggxiiQHIYQQo1TTxns2mDm7UzHV508Xias4EldxJK7izKa48p5jF/M8y/MmvqCswi4Dnqt0EEIIUaU+ADw/0YurKTmEgPcCx4BUhWMRQohqYQPnAP+B2T17QqopOQghhCgTGZAWQggxiiQHIYQQo0hyEEIIMYokByGEEKNIchBCCDGKJAchhBCjSHIQQggxSjVtnzEupdRngP8GvAX4W631985y7U3A7YAFPAl8KVv7+mznJhmXi6l78W5gGLhNa/3LAtd9Cfhc3qElwI+01v9VKbUS2AV0ZM7FtdaXTjamIuM6672VUncCn818+hOt9V1liutqYBNmgaQF/FhrfU/m3GeB/xt4PXP5Qa31qknEshzYBjQBPcANWut9Z1xjA/cBHwE84Fta6x+Nd24qJhjXncAnMYtGk8Dfa61/lTn3E+CDQHfm8u1a6y1liuvrwAbgzcyh32mtv5g5N6Gf/TTF9TDwjrxD7wCu0Vr/89linmJc3wHWAOcDb9da/7nANWX//YLZ13LYi/nP8IuzXaSUugD4GvA+YFnm32fGOzcFtwF9WuulwCeAHymlRhV11Vrfp7V+p9b6nZjV4LEzvpdXsuenmhiKiets91ZKrQDWAm/L/FubOVaOuDqBT2it3wb8H8AtSqkP5J3fnRdz0Ykh4wfA97XWy4HvAw8WuObTwFLM78r7gK8rpc6fwLmpmEhc/y/wXq31OzBvOv5RKeXknf9W3usz5cRQRFxgin1l753/R7aY38mSxqW1viHv/9+NwAngVxOIeSoeB1YAh85yTSV+v2ZXctBa/1lr/Qow3rv8a4HHtdaRTIvgh8B1Ezg3WdeR+WXMvFt5AfjoOM/5BHBMa/3CFO9d6rgKfY2HtdZDWush4GHK9Hpprfdord/MPD4F/IWRdcqnRCnVAlwCPJI59AhwiVLqzAJX1wE/1FqntdYRzH/4tRM4N61xaa1/pbWOZj59CdO6aprKvUsR1zhK8TtZirjWAz/XWk9rLWGt9fNa6yPjXFbW36+sWZUcirCYkZn6MLBoAuem435j+RymeZ1vuVLqRaXUHqXUjVOMqdi4xrr3jHi9lFIXAf878P/kHb5cKbVXKfVbpdTHJxHHIuANrXUKIPPxzQKxlPv3aaJx5bsBeE1rfTTv2H9VSv1JKfW4UuriKcZUbFyfVEq9pJT6tVLqfXnHK/56KaWCwH8GfjzBmKdbuX+/gCobc1BKvYh5MQppzf7wy228uCbx9c4B/opcPz7Ai8AirfWpTNfXbqXUG1rr3WWIq+h7n800vV5PABuyLQngl8A/aq2HlFLvAp5USl2htf7LZGKuZkqpy4G7gKvyDm/EtEzTSqkbgH9TSi0p0/+hHwBbtNZJpdRVwBNKqYu11j1luPdEXAMc1lrvzTs202MuuapKDlrrS0r0pQ4zsvthMXBkAucmFZdSKvs1I3lf8+mzPOVGYJfWOjtYiNa6L+/xQaXU48D7gTH/QJcqrnHuXdHXK9NlsBv471rr7Xn3yH/t/qiU+h3wv2G6nibqCHCeUsrWWqcyg3/nMvr7y8b7H3nxHprAucmaaFxk3uH+DLhaa62zx7XWb+Q9flgpdS+wcIqxTSgurXVn3uPfKKWOYMarniX3ek30/0rJ4srzOc5oNYwT83Qr9+8XMHe7lR4DrlFKNSulfMBNwD9N4NxkbQc+D6CUWoYZbP63s1y/jjN+OZVS5yilrMzjRuBDmAH4aY9rnHtvB25QSjmZwc4bKNPrpZRqAn4DfE9r/dAZ587Le9yO6XJ6qZggtNbHMd/npzKHPgX8MdO3e2a8NymlfJl+7GuARydwblImGpdS6r3APwLXaq1fPONc/uvzYcyMpjeYgiLiyr/3OzEzdbKJq9j/KyWLK3PPhZi6Bz8vIubpVtbfr6yqajmMRyn1KeDbwHzgaqXU3wEf0lq/opTaDLyptf6B1vqAUuou4A+Zp/4a8+6Ks52bgm8DP1FK7cf8J7xZa92fifl0XJnP3w/UMnKWBJjpbrcopZKYn9s2rfUTZYprzHtrrZ9RSu0AXs58zYe11lN9NzXRuP4OWA58Xin1+cxzv6u13gp8UZmprsOZ43+vtf7jJGL5ArBNKbUJM3vlhkwcu4BNmQkDPwUuBbJTIzdrrQ9mHp/t3FRMJK4HAAd4UCmVfd71Wus/ZZ7bipm80Qf8n1rrYaZuInF9Qyn1bszPNpGJKfvOfMyffRniAtNq/xet9Ykznn+2mCdNKXUfsBpow3TX9mit3zoDfr+knoMQQojR5mq3khBCiLOQ5CCEEGIUSQ5CCCFGkeQghBBiFEkOQgghRpHkIIQQYhRJDkIIIUaR5CCEEGKU/x9SshFYzgysAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x, f2,color='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9b99fc6a20>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x, f3,color='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9b99fe4ef0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x, f4,color='purple')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9]\n"
     ]
    }
   ],
   "source": [
    "sigmas = np.linspace(0.0,0.9,10)\n",
    "fs = [f1, f2, f3, f4]\n",
    "print(sigmas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.3165164\n",
      "4.428666\n",
      "4.693854\n",
      "11.412927\n",
      "5.0883727\n",
      "0.0,0 : 5.773359\n",
      "3.4128466\n",
      "3.8177392\n",
      "4.4555326\n",
      "4.4452915\n",
      "3.489471\n",
      "0.0,1 : 5.864722\n",
      "2.55121\n",
      "2.4870567\n",
      "3.3649533\n",
      "2.5808315\n",
      "3.5454357\n",
      "0.0,2 : 3.0371892\n",
      "1.0605474\n",
      "1.0484655\n",
      "1.8002052\n",
      "1.7783278\n",
      "2.7316294\n",
      "0.0,3 : 1.8558613\n",
      "1.6044647\n",
      "1.7972416\n",
      "1.6301302\n",
      "1.2586992\n",
      "1.9363227\n",
      "0.1,0 : 1.6577556\n",
      "2.5292113\n",
      "3.4724848\n",
      "2.9540653\n",
      "2.444877\n",
      "2.1020966\n",
      "0.1,1 : 2.363647\n",
      "1.2385798\n",
      "1.5869575\n",
      "1.392125\n",
      "1.4103067\n",
      "1.3495559\n",
      "0.1,2 : 1.5508937\n",
      "1.137523\n",
      "0.7532096\n",
      "0.82436013\n",
      "0.9533508\n",
      "1.2207271\n",
      "0.1,3 : 1.0978585\n",
      "0.9161378\n",
      "0.93390846\n",
      "0.85513234\n",
      "0.88875747\n",
      "0.9204679\n",
      "0.2,0 : 1.0572222\n",
      "1.4972677\n",
      "1.6500105\n",
      "1.563633\n",
      "2.1706228\n",
      "1.9646666\n",
      "0.2,1 : 1.6792473\n",
      "0.9622601\n",
      "0.7099171\n",
      "0.88597417\n",
      "0.9166153\n",
      "0.9260552\n",
      "0.2,2 : 0.97315335\n",
      "0.21291333\n",
      "0.5130028\n",
      "0.7539356\n",
      "0.45293054\n",
      "0.72957635\n",
      "0.2,3 : 0.5490277\n",
      "0.7204771\n",
      "0.7493786\n",
      "0.85244\n",
      "0.74890107\n",
      "0.9470168\n",
      "0.30000000000000004,0 : 0.74223465\n",
      "1.3280952\n",
      "0.85781586\n",
      "1.6996737\n",
      "1.5334388\n",
      "1.4874064\n",
      "0.30000000000000004,1 : 1.3006543\n",
      "0.56149685\n",
      "0.7939184\n",
      "0.7826102\n",
      "0.761603\n",
      "0.5918062\n",
      "0.30000000000000004,2 : 0.6528235\n",
      "0.07256753\n",
      "0.18316731\n",
      "0.24101302\n",
      "0.35792422\n",
      "0.23969722\n",
      "0.30000000000000004,3 : 0.3773468\n",
      "0.4716286\n",
      "0.65807617\n",
      "0.7351334\n",
      "0.568135\n",
      "0.4070482\n",
      "0.4,0 : 0.5394236\n",
      "1.0999154\n",
      "1.1869696\n",
      "0.9425587\n",
      "1.508071\n",
      "0.8805227\n",
      "0.4,1 : 1.0629547\n",
      "0.48446855\n",
      "0.6992607\n",
      "0.32096684\n",
      "0.57467395\n",
      "0.38139337\n",
      "0.4,2 : 0.49730837\n",
      "0.16985384\n",
      "0.31682673\n",
      "0.14539166\n",
      "0.18404447\n",
      "0.0037152618\n",
      "0.4,3 : 0.2407205\n",
      "0.35262096\n",
      "0.02848488\n",
      "0.4411731\n",
      "0.20091422\n",
      "0.39523944\n",
      "0.5,0 : 0.41392532\n",
      "0.92927027\n",
      "0.8733135\n",
      "0.81937736\n",
      "0.70997536\n",
      "0.84027994\n",
      "0.5,1 : 0.87138265\n",
      "0.51923275\n",
      "0.23628491\n",
      "0.19793582\n",
      "0.3079113\n",
      "0.21245015\n",
      "0.5,2 : 0.37166065\n",
      "0.110109136\n",
      "0.13376188\n",
      "0.12941448\n",
      "0.31277627\n",
      "0.031749252\n",
      "0.5,3 : 0.18949112\n",
      "0.44085586\n",
      "0.20953755\n",
      "0.2865927\n",
      "0.24141479\n",
      "0.23237923\n",
      "0.6000000000000001,0 : 0.324629\n",
      "0.70647216\n",
      "0.71640253\n",
      "0.6830268\n",
      "0.6746774\n",
      "0.87879884\n",
      "0.6000000000000001,1 : 0.7165672\n",
      "0.3911353\n",
      "0.22995684\n",
      "0.40184447\n",
      "0.33346593\n",
      "0.33557692\n",
      "0.6000000000000001,2 : 0.27176207\n",
      "0.10095255\n",
      "0.15070233\n",
      "-0.0036300272\n",
      "0.16898845\n",
      "0.10997343\n",
      "0.6000000000000001,3 : 0.14217764\n",
      "0.326396\n",
      "0.401862\n",
      "0.27543592\n",
      "0.30103853\n",
      "0.2734941\n",
      "0.7000000000000001,0 : 0.2505124\n",
      "0.7272493\n",
      "0.83806145\n",
      "0.76767933\n",
      "0.42282262\n",
      "0.7792771\n",
      "0.7000000000000001,1 : 0.6171741\n",
      "0.109162524\n",
      "0.35112542\n",
      "0.18418187\n",
      "0.10299401\n",
      "0.4145524\n",
      "0.7000000000000001,2 : 0.22408777\n",
      "0.055868365\n",
      "0.039873406\n",
      "0.08617143\n",
      "0.16341892\n",
      "0.08948879\n",
      "0.7000000000000001,3 : 0.10066611\n",
      "0.19749618\n",
      "0.24420461\n",
      "0.0783723\n",
      "0.32418668\n",
      "0.2992718\n",
      "0.8,0 : 0.19948366\n",
      "0.68093383\n",
      "0.5200536\n",
      "0.5599637\n",
      "0.62857056\n",
      "0.6669355\n",
      "0.8,1 : 0.5421426\n",
      "0.14672248\n",
      "0.32595232\n",
      "0.16835079\n",
      "0.21369377\n",
      "0.073559694\n",
      "0.8,2 : 0.16892713\n",
      "-0.007907551\n",
      "0.109723784\n",
      "0.09553514\n",
      "0.10128606\n",
      "0.026490275\n",
      "0.8,3 : 0.08995808\n",
      "0.23880677\n",
      "0.11562198\n",
      "0.17729264\n",
      "0.3021568\n",
      "0.16805547\n",
      "0.9,0 : 0.15108423\n",
      "0.5504997\n",
      "0.45780393\n",
      "0.45956063\n",
      "0.64887416\n",
      "0.42850533\n",
      "0.9,1 : 0.46416825\n",
      "0.22933817\n",
      "0.15017106\n",
      "0.23726618\n",
      "0.20050171\n",
      "0.13978177\n",
      "0.9,2 : 0.15220916\n",
      "0.02487325\n",
      "0.015485941\n",
      "0.0069098696\n",
      "-0.021917487\n",
      "0.032550007\n",
      "0.9,3 : 0.06090287\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "final_result = []\n",
    "for sigma in sigmas:\n",
    "    for fi, f in enumerate(fs):\n",
    "        data = np.concatenate([x.reshape(-1,1), (f + sigma * eps).reshape(-1,1)], axis=1)\n",
    "        mine_net = Mine().cuda()\n",
    "        mine_net_optim = optim.Adam(mine_net.parameters(), lr=1e-3)\n",
    "        result = train(data,mine_net,mine_net_optim,iter_num=int(5e+3))\n",
    "        result_ma = ma(result)\n",
    "        final_result.append(result_ma[-1])\n",
    "        print(str(sigma) + ',' + str(fi) +' : ' + str(final_result[-1]))\n",
    "        plt.plot(range(len(result_ma)),result_ma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.773359   1.6577556  1.0572222  0.74223465 0.5394236  0.41392532\n",
      "  0.324629   0.2505124  0.19948366 0.15108423]\n",
      " [5.864722   2.363647   1.6792473  1.3006543  1.0629547  0.87138265\n",
      "  0.7165672  0.6171741  0.5421426  0.46416825]\n",
      " [3.0371892  1.5508937  0.97315335 0.6528235  0.49730837 0.37166065\n",
      "  0.27176207 0.22408777 0.16892713 0.15220916]\n",
      " [1.8558613  1.0978585  0.5490277  0.3773468  0.2407205  0.18949112\n",
      "  0.14217764 0.10066611 0.08995808 0.06090287]]\n"
     ]
    }
   ],
   "source": [
    "re_final_result = np.transpose(np.array([final_result[4*i: 4*i+4]  for i in range(10)]))\n",
    "print(re_final_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f9b9b0ff358>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(re_final_result,cmap=\"YlGnBu\",linewidths=.5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
